Okay. Every country has good openings and bad openings. The only difference is that if you choose a bad Austrian opening, you will probably not see 1904. As such, choosing a good one is very important! You may still not live until 1904, but at least you will have tried your best.
Firstly, it's important to look at who you border. Austria borders four different countries, which is a huge number - as such, your first priority as Austria should be to secure alliances with at least two of your neighbors, and preferably all four.
If Germany is at all competent, he will immediately agree to an alliance with you, and will not stab you until at least the middle of the game. Germany also borders four countries, and is generally at war with at least one of England or France by 1903, so he can ill afford to plunge into Austria and leave his back open. In addition, he is likely to give you any non-military aid he can, as he much enjoys having the panicked, beset-on-all-sides Austria neighboring him, who can act as a buffer. Don't worry about Germany.
Russia also is likely to come into contact with four different nations at the start of the game, but unlike Germany, Russia is unlikely to have your best interests at heart. A good Russia will secure a non-aggression pact with Germany from the outset, leaving the Kaiser free to play in the west; this means that Russia has two main outlets for expansion, Scandinavia and the Balkans, and if Russia can jump into Austria and get a huge foothold in the region, so much the better for her. On the other hand, Russia can easily gain territory by invading Turkey with your help. She'll probably do whichever is easier.
This means that you should propose an Austria/Russia alliance against Turkey as soon as possible, whether you intend to follow through or not. This also means that if you decide to DMZ Galicia like a dumbass, don't be all surprised when the Russians march in in Spring 1901.
First rule of Austria: Army Vienna to Galicia. Always. 100%. Whether you tell Russia about this, of course, is up to you - I like to do so, as a planned bounce, as it builds up your credibility if you say "I'm moving to Galicia," and, indeed, move to Galicia. If you're a gambler, then you can move to Budapest instead, but if you're facing a good Russia she will end your game with this mistake.
Oh, and Rumania is customarily Russia's, so be aware that if you bounce her out of there she will be upset with you.
Next, there is Turkey. Turkey, unlike the previous countries I just listed, has only two neighbors: Russia, and Austria. Three, if you count Italy, but that is really stretching it. All of Turkey's opportunities for expansion lie in the Balkans, and as such Turkey is going to want to either kill you with the help of Russia or kill Russia with the help of you, at which point he will either stab his ally or start pumping out fleets and rushing toward Italy.
This, of course, doesn't mean that he isn't a useful ally. Turkey's strong corner position can allow you two to dominate the Balkans together, and eventually march on Russia proper. And, of course, if you happen to manufacture a conflict between the Turks and the Russians, you can easily take advantage of the fray. In the end, Diplomacy is more about the players than it is about moving pieces around, anyway, so if you like the looks of Turkey as an ally, then go for it.
Finally, there is Italy. Italy is a really boring country, and people complain about it even more than they complain about Austria. (Hey, at least Austria has an exciting, if short, life!) Italy also has about three directions it can go in; it can attack France, it can attack you, or it can attack Turkey with your help. You, obviously, want it to do one of the ones in which it doesn't attack you.
The first way is just to not be an appealing target. Say you're ordering Trieste -> Venice turn 1, and do so; this stops any attack on Austria before it begins, and encourages Italy to go mess with France in Piedmont instead of thinking he can just walk into Trieste. Ask Germany if he's invading France; tell Italy that Germany plans to invade France no matter what he says. If he doesn't go West he'll go East, and that can only end in tears.
Well, tears or the Lepanto. The Lepanto Opening is a famous Diplomacy opening in which in Fall of 1901, Italy convoys into Tunis and builds a second fleet, then invades Turkish waters. In the Autumn of 1902, Italy convoys the army in Tunis into Syria, and, attacked on both sides, Turkey quickly crumbles. A full discussion of the Lepanto is beyond the scope of this post (just Google it if you don't know what it is; every Diplomacy player should at least be able to recognize one), but let it be said that the Lepanto is a solid opening that leaves you a bit vulnerable in the Spring of 1901, but makes up for it by quickly demolishing Turkey and leaving you with only three neighbors to deal with.
So, that's your allies. Now, let's look at your three units. It is in theory really obvious where they should all go in the Spring of 1901, but since so many people get it wrong I figured I'd explain anyway.
The Army in Vienna, as I mentioned previously, should go to Galicia. Always. Even if you're allying with Russia. Especially if you're allying with Russia. (Just tell her first.) If Russia gets Galicia in the Spring of 1901, you aren't going to last very long at all. So don't let her.
The Army in Budapest has more options. Oh, did I say that out loud? Oops, I lied. Must be playing too much Diplomacy, I guess. Anyway, where was I? Oh, right, Budapest. You only have one option here: go to Serbia. Otherwise, Turkey will just bounce you out of there from Bulgaria in the fall, you will get no builds in 1901, your neighbors will smell weakness (they already smell fear - c'mon, you're Austria for crying out loud, they always smell fear) and you will die a horrible death. Perhaps I'm being a bit melodramatic, but seriously: go to Serbia.
Your only alternative is to go to Rumania, and that doesn't do very much for you. If Russia moves to Rumania, then you bounce, tick off Russia, get bounced out of Serbia in the fall (if Turkey says otherwise he's lying), etc., etc. If Russia moves to the Black Sea instead (that is, if Russia is SANE), then you get Rumania! Except that if Russia moves Moscow to Ukraine in the Spring, and 90% of Russians do, then you'll just end up getting kicked out of Rumania anyway, and will have accomplished nothing for all of your effort except to annoy Russia.
The Fleet in Trieste has two main options: either it should go to Venice or it should go to Albania. Going to Venice secures you against an Italian attack, while going to Albania allows you to acquire Greece in 1901 (assuming you moved to Serbia from Budapest, which you should have). Which one you choose depends on your evaluation of the likelyhood of Italy walking into Trieste. But certainly, no matter which one you choose, you should tell Italy that you'll be ordering Trieste -> Venice! This reduces the effectiveness of any Austrian attack the Italian can muster, which makes alternatives more attractive. Like an attack on France, a Lepanto opening if you're willing, or a classic Italian "sit there with four centers until someone big and tough kills you." There are a lot of that last one on this site!
Anyway, hopefully you now know how to survive until 1902 with Austria. I'll leave you with a bit of philosophical advice: If you come to a fork in the path of life, take the road less traveled by. Or the one more traveled by. Whichever one leads to Galicia.
Good night!
An apology to Xyanth
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